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Complex Function Differentiability

Chanapat Pacharapokin; Hiroshi Yamazaki; Yasunari Shidama; Yatsuka Nakamura — 2009

Formalized Mathematics

For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.

The Cauchy-Riemann Differential Equations of Complex Functions

Hiroshi Yamazaki; Yasunari Shidama; Yatsuka Nakamura; Chanapat Pacharapokin — 2009

Formalized Mathematics

In this article we prove Cauchy-Riemann differential equations of complex functions. These theorems give necessary and sufficient condition for differentiable function.

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